a. A convex mirror has a radius of curvature whose magnitude is 51 cm. The mirro
ID: 1474723 • Letter: A
Question
a. A convex mirror has a radius of curvature whose magnitude is 51 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 8.0 cm long fluorescent lamp oriented vertically is placed at +102 cm. What is the focal length of the mirror?
b. At what distance from the mirror can we find a sharp image of the lamp?
c. How tall is the image of the lamp?
d. If the convex mirror were replaced by a plane mirror and the lamp moved to 226 cm from the plane mirror, how tall would the image be?
Explanation / Answer
a)
R = radius of curvature = 51 cm
focal length is given as
f = R/2 = 51/2 = 25.5 cm
b)
do = object distance= 102 cm
di = image distance
using the mirror equation
1/f = 1/di + 1/do
1/(-25.5) = 1/di + 1/102
di = 20.4 cm
c)
ho = height of object = 8 cm
hi = image height
Using the formula
hi/ho = - di/do
hi/8 = - (-20.4) / 102
hi = 1.6 cm
d.
image height = 8 cm.
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